Mathematics · Topology
Let X be an uncountable set. Let the topology on X be defined by declaring a subset U ⊆ X to be open if X - U is either empty, finite, or countable, along with the empty set. Then, which of the following statements is TRUE?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Every compact subset of X is closed
- 2Every closed subset of X is compact
- 3X is T1 (singleton subsets are closed) but not T2 (Hausdorff)✓
- 4X is a Hausdorff space (T2)
Correct answer
X is T1 (singleton subsets are closed) but not T2 (Hausdorff)
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